SOLUTIONS

BUILTIN MATHEMATICA SYMBOL
GraphPlot
GraphPlot[{v_{i1}>v_{j1}, v_{i2}>v_{j2}, ...}]
generates a plot of the graph in which vertex is connected to vertex .
GraphPlot[{{v_{i1}>v_{j1}, lbl_{1}}, ...}]
associates labels with edges in the graph.
GraphPlot[m]
generates a plot of the graph represented by the adjacency matrix m.
Details and OptionsDetails and Options
 GraphPlot attempts to place vertices to give a well laidout version of the graph.
 The vertex names and the labels can be any expressions.
 With the default setting DirectedEdges>False, edges are drawn as ordinary lines. With DirectedEdges>True, edges are drawn as arrows.
 GraphPlot has the same options as Graphics, with the following additions and changes:

DataRange Automatic the range of vertex coordinates to generate DirectedEdges False whether to show edges as directed arrows EdgeLabeling True whether to include labels given for edges EdgeRenderingFunction Automatic function to give explicit graphics for edges Frame False whether to draw a frame around the plot FrameTicks None what ticks to include on the frame Method Automatic the method used to lay out the graph MultiedgeStyle Automatic how to draw multiple edges between vertices PackingMethod Automatic method to use for packing components PlotRangePadding Automatic how much padding to put around the plot PlotStyle Automatic overall graphics directives for vertices and edges SelfLoopStyle Automatic how to draw edges linking a vertex to itself VertexCoordinateRules Automatic rules for explicit vertex coordinates VertexLabeling Automatic whether to show vertex names as labels VertexRenderingFunction Automatic function to give explicit graphics for vertices  With the default setting VertexLabeling>Automatic, vertices are displayed as points, with their names given in tooltips, so long as the number of vertices is not too large.
 Tooltip[v_{k}, vlab] can be used to specify an alternative tooltip for a vertex. Tooltip[v_{i}>v_{j}, lbl] specifies a tooltip for an edge.
 Explicit settings for VertexRenderingFunction and EdgeRenderingFunction override settings for VertexLabeling, EdgeLabeling, and DirectedEdges.
 With VertexRenderingFunction>f, each vertex is rendered with the graphics primitives given by , where is the position where the vertex is being placed, and is its name.
 With EdgeRenderingFunction>g, each edge is rendered with the graphics primitives given by , where , are the beginning and ending points of the edge, , are the beginning and ending vertices, and the is any label specified for the edge.
 The graphics primitives obtained by applying EdgeRenderingFunction and VertexRenderingFunction are in effect directly spliced into the graphic generated by GraphPlot. Inset can be used to insert an arbitrary expression.
 In the graphics generated by GraphPlot, edges are effectively drawn first, and vertices afterwards.
 With the default setting DataRange>Automatic, coordinates are chosen so that the average length of the edges in the graph is approximately 1.
 In VertexCoordinateRules, an explicit rule specifies coordinates for a vertex. If any coordinate is given as Automatic, it is found automatically. Vertices for which no rules are specified are taken to have automatically generated x and y positions.
 The graph does not need to be connected. Disconnected components are typically arranged so as to fill area roughly uniformly.
 When a graph is specified by an adjacency matrix, the names of its vertices are taken to be successive integers starting at 1.
 The adjacency matrix m in GraphPlot[m] can be a SparseArray object.
 With the default setting MultiedgeStyle>Automatic, multiple edges are not shown if the graph is specified by an adjacency matrix.
 Possible settings for Method include , , , , , and . The method lays out all vertices on a single line.
 With Method>Automatic, GraphPlot normally uses the method, though it uses the method if the graph is a tree.
 GraphPlot returns an object of the form Graphics[Annotation[data, VertexCoordinateRules>rules]].
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